Assignment: Mathematical Statistics

Problem Set

1. A department store chain randomly sampled 10 stores in a state. After a review of sales records, it was found that compared with the same period last year, the following percentage increases in dollar sales had been achieved over the Christmas period this year:

10.2  3.1  5.9  7.0  3.7  2.9  6.8  7.3  8.2  4.3

a. Find the mean percentage increase in dollar sales
b. Find the median.
c. Find the sample variance.
d. Find the sample standard deviation.
e. Find the coefficient of variation.
f. Find the range.
g. Find the interquartile range.

2. Sheila Newton, an investment counselor, has reported the following annual growth rates in the price of a particular stock:

4.3 %, 6.0 % , 3.5 % , 8.2 % , 7.0 %

a. What is the mean growth rate over the five-year period? (Note: When finding the geometric mean for these percentage growth problems, you will have to convert the percentages to decimals, add a one, calculate the geometric mean, and then subtract one from your calculation and convert back from a decimal to a percent.)

b. If this growth rate continued, how many years would be required for the price to double?

3. A sample of the 3-year annualized returns for 14 low-risk mutual funds yielded the following data:

31.50  12.46  9.77  22.47  18.47  15.47  38.16  20.72  13.8  21.49  11.35  17.48  18.61  18.37

a. Find the arithmetic mean.
b. Find the median.
c. Find the range.
d. Find the first quartile.
e. Find the third quartile.
f. Find the interquartile range.